Express this quotient in scientific notation: ${\frac{5.100\times 10^{2}} {6.0\times 10^{-1}}}$
Start by collecting like terms together. $= {\frac{5.100} {6.0}} \times{\frac{10^{2}} {10^{-1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.85 \times 10^{2\,-\,-1}$ $= 0.85 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.85$ is the same as $8.50 \div 10$ , or $8.50 \times 10^{-1}$ $ = {8.50 \times 10^{-1}} \times 10^{3} $ $= 8.50\times 10^{2}$